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Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 301 / 2 / iv

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2018 iii Paper 301 2
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iv
The canonical quantization of a real scalar field promotes the classical equal-time brackets to the canonical commutation relations, in units ℏ=1:
[ϕ1​(t,x),ϕ1​(t,y)][π1​(t,x),π1​(t,y)][ϕ1​(t,x),π1​(t,y)]​=0,=0,=iδ(3)(x−y).​​
(1)
The Dirac delta distribution expresses locality of the conjugate variables. These are identities of operator-valued distributions, interpreted after spatial smearing where necessary.

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